They're there to help.

You can choose "No Barbarians" and the Tribal Barbarians will not spawn, as there will be no Encampments on the map. Until you can build State-Sponsored Encampments (at currency), there will be no camps to evolve.

Place a State-Sponsored Encampment where you would like a new city to spawn, and wait. Once the Evolution timer comes due, the State-Sponsored Encampment should evolve into a new city for you.

Similar problem here. I think something is going wrong. I tested this several times. I wanted to play as barbarian. I choose custom game and check "play as barbarians". First thing i see is -nothing. Klicking "next round" i got my own barbarian city and one unit standing outside the borders. But this unit belongs to AI barabarian and is moving away. I have to wait several rounds building my own first unit. I'm not sure of this but i believe barbarian AI attacked me first. Strange thing, i can attack AI barbarian units but not their camps.

Yes, the AI Barbarians (which I call "Tribal") are still there. You are at peace with them. They will attack cities, capture them, and give them to you.

They'll eventually die out, as there will be no more places for their Encampments to spawn. Occasionally, their Encampments will evolve into a new city for you.